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<p><dfn class="terminology">Example 3</dfn> If assume different boundary conditions</p>
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\begin{equation*}
{y(0)=0,\quad y(\pi)=0}.\vspace{-0.2cm}
\end{equation*}
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<p class="continuation">Then <span class="process-math">\(c_1=0\text{,}\)</span> <span class="process-math">\(c_2\)</span> can be arbitrary, so <span class="process-math">\(y(x) = c_2 \sin x\)</span> is a solution for any <span class="process-math">\(c_2\text{.}\)</span> There are <em class="emphasis">infinitely many solutions</em>.</p>
<span class="incontext"><a href="sec7_1.html#p-309" class="internal">in-context</a></span>
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